用调和函数构造解析函数的简便方法

:1004-2261(2001)S1-004-02,(,300380):f(z)=u+ivz.:;;z:O17415:BXSimplewayofforminganalyticfunctionfrombarmonicsXUMin2hui,MENGXiang2fa(VocationalTechnologyCollege,TianjinInstituteofTechnology,Tianjin300380,China)Abstract:Thisarticlemainlytalksaboutakindofsimplewaywhichtransformsanalytiefun2vtionf(z)=u+ivintocomplexvariablez.Keywords:anaryticfunction;harmonics;complexvariablez,u(x,y)(v(x,y))f(z)=u+iv3,..,,f(z)=9u9x+i9v9xz,.,f(z)z.,,,z.,x+iy,,,x+iy,y=0,x,z.,y=0z.,f(z),f(z).f(z)=9u9x+i9v9xy=0f(z)z..[1].1u=(x-y)(x2+4xy+y2),f(z)=u+ivf(z)=(x-y)(x2+4xy+y2)+iv,9u9x=x2+4xy+y2+(x-y)(2x+4y)9u9y=-(x2+4xy+y2)+(x-y)(4x+2y):f(z)=9u9x-i9u9y=x2+4xy+y2+(x-y)(2x+4y)-i-(x2+4xy+y2)+(x-y)(4x+2y)y=0xz,f(z)=3(1-i)z2z,f(z)=(1-i)z3+c(c)2v=ex(ycosy+xsiny)+x+y,f(z)=u+ivf(0)=0f(z)=u(x,y)+iex(ycosy+xsiny)+x+y1720019JOURNALOFTIANJININSTITUTEOFTECHNOLOGYVol.17Suppl.1Sept.2001X:2001-06-25:(1955-),,9v9x=ex(ycosy+xsiny+siny)+19v9y=ex(cosy-ysiny+xcosy)+1,f(z)=9v9y+i9v9x=ex[(x+1)cosy-ysiny]+1+i[exycosy+(x+1)exsiny+1]y=0,xz,f(z)=ez(z+1)+1+izf(z)=[ez(z+1)+1+i]dz=zez+(1+i)z+c.(c)f(0)=0c=0,f(z)=zez+(1+i)z:[1].[M].:,1999.(3)M2n2{1,6,1},2x+6y+z-20=0Tx+3y-10=0x+6y+z-20=02x2+y2+z2-3x=0[2]2x-3y+5z-4=0M(1,1,1).x2+2y2+z2-3x=0M1x-2y-2z+3=0,2x-3y+5z-4=0,22x-3y+5z-4=0,Tx-2y-2z+3=02x-3y+5z-4=0{1,-2,-2}{2,-3,5}=-{16,9,-1},16x+9y-z-24=0:[1].[M].:,2000.5.[2].[M].:,1996.12.5: